"That we cannot speak about an absolute rest of the aether, is self-evident; this expression would not even make sense. When I say for the sake of brevity, that the aether would be at rest, then this only means that one part of this medium does not move against the other one and that all perceptible motions are relative motions of the celestial bodies in relation to the aether." -Henrik Lorentz

- Mathematically Compatible but Conceptually Incompatible -

It is important to note that it is generally accepted in the physics community that there is no major distinction between Lorentz Ether Theory(LET) and Special Relativity(SR) and that SR is only preferred because it does not make mention of a substance which cannot be detected. This is patently absurd. They only believe this because the math is the same and it is well known that Einstien based his papers upon Lorentz's. Relativity used to be known as "Lorentz-Einstein Relativity". Lorentz created an illusion based upon an underlying reality and Einstein expounded upon the illusion while being ignorant of the reality.

"On the Electrodynamics of Moving Bodies" These effects we've described on the previous pages are wildly different from Special Relativity. Furthermore, the above simple calculations show, if reading through OEMB and sound is substituted for light in Einstein's procedures for clock synchronization, the same results will occur with this physical wave. Therefore, if LET is considered, the assertion at the end of section 2 in OEMB is fallacious if based solely only upon the previous derivation and thought experiments. IE: The assumption of a lack-of-simultaneity will still seem to apply to sound given his reasoning, but it is asinine to assume sound travels as a frame-indepedant “constant” simply because you can arrange clock synchronizations in such a way when shortening is involved.

He asserts that the idea of absolute simultaneity cannot have any meaning given his clock sychronization procedure, however, we can now see that the concept of absolute simultaneity can exist, but go undetected or unnoticed or misunderstood. This is the point at which Einstein's logic failed: He saw Lorentz's illusion and believed it to be reality. He assumed that if Lorentz was correct, and we could not detect the true reference frame and therefore true simultaniety, then scientifically speaking, something that cannot be proven experimentally is not part of science. Do you understand the dilemma here? Einstein decided that we must utterly ignore the presumed reality underneath the illusion because we've determined that we cannot detect it.

His "derivation", or assertion, of non-simultaneity is obviously fallacious if it also applies to sound. Furthermore, the presumptions which follow non-simultaneity, especially the absolute equality of frames, are also, therefore, fallacious logically in consideration of LET. Therefore because of the presumption of an ether, LET and SR on not equivalent but in-fact, contradictory. The existence of an ether causes the primary assumption of SR and its subsequent assertions to be invalid. The theories are mathematically compatible but conceptually incompatible.

- Paradoxes: SR Has 'Em, LET Don't -

Frame-independant constancy (or just constancy of light as they call it) is the reason for the twins paradox and the reason the twins paradox does not exist in LET because the true transformation from one perspective to another requires an assumption of a single universal frame and if converting to a slower frame from a faster frame, one must invert all calculations of the transformation. This is not true in SR. It is important to note, however, that LET assumes this differentiation between faster and slower frames, though it exists, is impossible to determine (detect and test) and therefore cannot be discussed in a purely scientific way. It is also obvious, and therefore a scientist such as Lorentz would find no need to discuss the elementary mathematics of inverting a calculation.

The idea of a cummutable calculation should be obvious to anyone past grade school. Unfortunately, Einstien only discussed one perspective without realizing that his assertions that only one perspective was necessary, would lead to a situation in which the math becomes non-commutable. IE: Einstein though that it was unnecessary to discuss more than one perspective when they are all the same. It only becomes a paradox when you discuss two perspectives simultaneously which only happened long after OEMB was published.

The twins paradox is only currently “solved” in modern apologetics by eliminating the difference between LET and SR and is therefore not a solution at all. Once a single universal frame is established by stating that one twin is, in-fact, older than the other, the theory is reduced to a fully invertible situation such that the proper way to convert from the traveling twin to the stationary twin is to invert the transformation. This is counter to SR. (Incidentally, this also makes light constant in only one frame)

IE: when we "solve" the twins paradox the way we are told to by the modern physics community, by simply assuming that the "accelerated" twin is the one who is truly in motion and therefore aging less, it becomes obvious that from his perspective during the trip that he could look out his window towards earth with a telescope and see his twin run around aging faster. This infers a universal frame and eliminates everything SR adds beyond LET.

- Describing the Difference Mathematically -

The calculations we derived earlier fully account for the motion of a moving observer within his observations. EG: Using the transformation accounts for his motion when predicting what he observes. The numbers he observes have been altered by his motion. His perceptual differences are a representation - a different form of his motion. This means that in LET, if two observers both consider themselves stationary and the other to be moving, and as a consequence, both apply the Lorentz transformation without one of them using an inversion, the final effect of both calculations considered simultaneously is a duplication of motion. Therefore, according to LET, when SR considers two frames perfectly equivelent it duplicates motion. It occurs because mathematically, each observer has their own reference frame. Two reference frames results in two sets of motion when considered together. This is simply another representation, or form of, the twins paradox.

"How can the two theories be mathematically indistinguishable but also mathematically different? You're not making sense." The answer is two-fold: First, it is because the way you apply the math is different. Second, it is because both theories agree that the resting ether frame cannot be known and is therefore technically unscientific to discuss. We now see the flaw in this assertion because discussion of the ether is required to formulate an "a priori" logic proof. This fundamental difference between the theories -the duplication of motion- can only be mathematically seen when considering the arrival of a wave at a distant point as follows.

If we revert to our alien sound experiment detailed previously, we can consider the following extension to the experiment: First let us define a “sound-minute” as the distance sound travels in one minute. Let us also assume that the experiment is outfitted with clocks that use reflected sound chirps in place of a pendulum and are also made from the same flexible material the aliens use. Therefore we know from our derivation that these clocks will be length contracted and time dilated by gamma.

Let us also place a receiver at a distance from the truck in the direction it is traveling at .5c. In the frame of the ground, the emitter lets out a chirp exactly .5 sound-minutes away from the distant receiver. The time interval marked on the ground clocks for the arrival of the fist wavefront of sound will be exactly .5 minutes. The period of time marked on the moving clocks will be .433 minutes.

Let us say that one of these alien scientists named Labret Neetsiin, who has never experienced an atmosphere believes that since their experiments have never been capable of detecting the atmosphere, the idea of an atmosphere is unnecessary. Instead, the area near planets simply conducts sound and has a crushing effect on objects nearby. Sound travels the same speed to all moving observers so therefore c can simply be treated as a frame independent constant. As such, just like the rest of the universe and a principle they call Lagleani Relativity, all physical phenomena in a given frame can be treated equally to any other frame. The atmosphere frame is unnecessary and irrelevant.

Now If we treat this same situation with this new principle of relativity which is an assumption of exactly equivalent frames, the moving observer/clock considers itself stationary and the distant receiver to be moving toward it at .5c (even if he is ignorant of the ground/air frame) It is approaching from a distance of .433 sound-minutes away. Therefore the period of time it would take for the chirp to reach the distant emitter would be the distance less the speed of the approaching emitter for a total of .288 sound minutes.

Because we understand physical waves, we know that Neetsiin is in error with a calculation of .288 instead of .433 but he can never know this fact with his current idea and stretchy equipment without testing out his calculation. Unfortunately this is where the metaphor and reality diverge because Neetsiin could test it out and find out that he's wrong but we can't test out Einstein's idea because we lack the technology.

As you can see, by assuming the equivalence of frames, the motion of the truck is calculated twice. What is created is actually a self-referential loop that we only went through once but could continually be followed for an ever-deminishing result. It is a logic error in the theory itself but not in the math which describes it. If this was a computer program, I would call it a "potential memory leak".

Additionally, while I did present that the moving frame would measure a .433 distance because this is true of SR, I did not mention that this is also another irrational result of perfect frame equality. Without a rest frame, "shorter" and "longer" are equivelent because there is no reference. Einstein shortens the entire frame instead of only the physical objects in it as Lorentz would. Instead of measuring the same distance with a short ruler and therefore measuring more total space, less space is measured. In this way, the frame is both shorter and longer simultaneously but this confusing truth is a subject for a different page. This shortening of all of reality (instead of just physical objects), in combination with the requirement that the same light travels in both frames (that it is one real event in one reality) requires any justification of SR to cause an irrational split in reality which then leads to the irrational and unnecessary addition of another dimention, lack of simultaneity and all the other paradoxes of SR which are not present in LET.
(An interesting side note is that the duplicated result is equivalent to the "downstream" trip alone of a shortened interferometer experiment at any given speed and change factor.)

- The Final Summary -

The single difference between the two theories is a single universal reference frame versus more than one reference frame. The additional frames lead to frame-independant constancy as a reality instead of an illusion. This in-turn leads to a lack of simultaneity. From the perspective of a classical theory (no weird or counter-intuitive effects) special relativity duplicates motion. It does this because both frames taken together are equivalent to having two universal frames. This is the reason for the twins paradox.

Once again we find that LET and SR are incompatible. In all mathematical situations other than the one outlined above (the arrival time at the distant receiver) the two theories are the same. The situation above, however, can only be understood when one looks behind the curtain of Lorentz's illusion. IE It can only be seen if one actually knows where the medium is at-rest which Lorentz considered to be impossible because the illusion was impossible to penetrate via experiment. Therefore, in all ways, LET and SR are "technically" mathematically compatible because the preferred frame is impossible to determine. In LET it is assumed that the curtain of illusion is impenetrable.

It is only the understanding of the concepts alone, without the math, that reveals the difference. The concepts reveal what the math hides. Only reasoning can reveal what can never be discovered mathematically.